EVENT DETAILS AND ABSTRACT

Title: On confining potentials and essential self-adjointness for Schroedinger operators on bounded domains
Speaker: Professor Irina Nenciu
Speaker Info: University of Illinois at Chicago
Brief Description:
Special Note: http://www.math.uic.edu/~acheskid/PDEworkshop.html
Abstract:

Let $\Om$ be a bounded domain in $\IR^n$ with $C2$-smooth boundary, $\partial\Om$, of co-dimension 1, and let $H=-\Delta +V(x)$ be a Schr\"odinger operator on $\Om$ with potential $V \in L^{\infty}_{loc}(\Om )$. We seek the weakest conditions we can find on the rate of growth of the potential $V$ close to the boundary $\partial\Om$ which guarantee essential self-adjointness of $H$ on $C_0^\infty(\Om)$ . As a special case of an abstract condition, we add optimal logarithmic type corrections to the known condition $V(x)\geq \frac{3}{4d(x)2}$ where $d(x)=\text{dist}(x,\partial\Om)$. The proof is based on a refined exponential Agmon estimate combined with a well known multidimensional Hardy inequality.